Function suggests nano-structure: towards a unified theory for secretion rate, a statistical mechanics approach

Abstract

The inventory of secretory granules along the plasma membrane can be viewed as maintained in two restricted compartments. The release-ready pool represents docked granules available for an initial stage of fast, immediate secretion, followed by a second stage of granule set-aside secretion pool, with significantly slower rate. Transmission electron microscopy ultra-structural investigations correlated with electrophysiological techniques and mathematical modelling have allowed the categorization of these secretory vesicle compartments, in which vesicles can be in various states of secretory competence. Using the above-mentioned approaches, the kinetics of single vesicle exocytosis can be worked out. The ultra-fast kinetics, explored in this study, represents the immediately available release-ready pool, in which granules bound to the plasma membrane are exocytosed upon Ca(2+) influx at the SNARE rosette at the base of porosomes. Formalizing Dodge and Rahamimoff findings on the effect of calcium concentration and incorporating the effect of SNARE transient rosette size, we postulate that secretion rate (rate), the number (X) of intracellular calcium ions available for fusion, calcium capacity (0 ≤ M ≤ 5) and the fusion nano-machine size (as measured by the SNARE rosette size K) satisfy the parsimonious M-K relation rate ≈ C × [Ca(2+)](min(X,M))e(-K/2).

Keywords: SNARE; cellular communication; granule size; intracellular calcium; secretion rate.

Figure 1.

Scattergram analysis of granule size (, equivalent to SNARE rosette size) as associated with maximal secretion rate. For a tabulated data list, see the electronic supplementary material, table S1. The regression of ln(rate) on K − 1 is 10.4893 − 0.4848 × (K − 1), or rate ≈ 36000 × 0.6158^{K −1}. The role of Ca²⁺ should, in principle, explain the heterogeneity within the blocks shown in the figure, but the crucial effect of K in the figure is well explained by the G&E model described previously by the authors [5,16].